Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 5x - 9$ and $ BC = 7x - 25$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {5x - 9} = {7x - 25}$ Solve for $x$ $ -2x = -16$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 5({8}) - 9$ $ BC = 7({8}) - 25$ $ AB = 40 - 9$ $ BC = 56 - 25$ $ AB = 31$ $ BC = 31$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {31} + {31}$ $ AC = 62$